College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 2 - Section 2.4 - Circles - 2.4 Assess Your Understanding - Page 187: 50


$A=36\pi-72$ sq.units

Work Step by Step

The diagonal of the square equals the diameter of the circle. From the equation, r=6, diameter = 12 The sides a of the square and the diagonal d satisfy Pythagorean theorem $a^{2}+a^{2}=d^{2}$ $2a^{2}=12^{2}$ $a^{2}=\displaystyle \frac{144}{2}=72$ $a^{2}$ is the area of the square.... $A_{sq}=72$ sq.units This area is subtracted from the area of the circle, $A=A_{circ}-A_{sq}$ $A=6^{2}\pi-72$ $A=36\pi-72$ sq.units
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